Journal of Function Spaces The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Hyers-Ulam Stability of the First-Order Matrix Differential Equations Mon, 30 Nov 2015 08:26:39 +0000 We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equations . Moreover, we apply this result to prove the generalized Hyers-Ulam stability of the th order linear differential equations with variable coefficients. Soon-Mo Jung Copyright © 2015 Soon-Mo Jung. All rights reserved. The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators Wed, 25 Nov 2015 14:07:30 +0000 Let be a Schrödinger operator acting on , , where is a nonnegative locally integrable function on . In this paper, we will first define molecules for weighted Hardy spaces associated with and establish their molecular characterizations. Then, by using the atomic decomposition and molecular characterization of , we will show that the imaginary power is bounded on for , and the fractional integral operator is bounded from to , where , , and . Hua Wang Copyright © 2015 Hua Wang. All rights reserved. Lebesgue Decomposition Theorem and Weak Radon-Nikodým Theorem for Generalized Fuzzy Number Measures Wed, 25 Nov 2015 05:34:17 +0000 The Lebesgue type decomposition theorem and weak Radon-Nikodým theorem for fuzzy valued measures in separable Banach spaces are established. Cai-Li Zhou and Fu-Gui Shi Copyright © 2015 Cai-Li Zhou and Fu-Gui Shi. All rights reserved. Necessary and Sufficient Conditions for Inner Functions to Be in -Spaces Tue, 24 Nov 2015 07:51:48 +0000 Under some regularity conditions on , inner functions in -spaces are characterized in the following way: an inner function belongs to if and only if it is a Blaschke product associated with satisfying , where . The result generalizes earlier theorems in (Essén et al., 2006) and (Pérez-González and Rättyä, 2009). Atte Reijonen Copyright © 2015 Atte Reijonen. All rights reserved. Topological Structures of Derivative Weighted Composition Operators on the Bergman Space Wed, 18 Nov 2015 08:30:00 +0000 We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linear-fractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology. Ce-Zhong Tong, Cheng Yuan, and Ze-Hua Zhou Copyright © 2015 Ce-Zhong Tong et al. All rights reserved. Categories of -Fuzzy Greedoids Tue, 10 Nov 2015 07:34:07 +0000 The concepts of -greedoids, fuzzifying greedoids, and ()-fuzzy greedoids are introduced and feasibility preserving mappings between greedoids are defined. Then -feasibility preserving mappings, fuzzifying feasibility preserving mappings, and ()-fuzzy feasibility preserving mappings are given as generalizations of feasibility preserving mappings. We study the relations among greedoids, -greedoids, fuzzifying greedoids, and ()-fuzzy greedoids from a categorical point of view. Zhen-Yu Xiu and Fu-Gui Shi Copyright © 2015 Zhen-Yu Xiu and Fu-Gui Shi. All rights reserved. The Randomized American Option as a Classical Solution to the Penalized Problem Tue, 27 Oct 2015 08:11:12 +0000 We connect the exercisability randomized American option to the penalty method by showing that the randomized American option value is the unique classical solution to the Cauchy problem corresponding to the canonical penalty problem for American options. We also establish a uniform bound for , where is the infinitesimal generator of a geometric Brownian motion. Guillaume Leduc Copyright © 2015 Guillaume Leduc. All rights reserved. Formulae for the Generalized Drazin Inverse of a Block Matrix in Banach Algebras Wed, 21 Oct 2015 12:18:34 +0000 We present some new representations for the generalized Drazin inverse of a block matrix in a Banach algebra under conditions weaker than those used in resent papers on the subject. Xiaoji Liu and Xiaolan Qin Copyright © 2015 Xiaoji Liu and Xiaolan Qin. All rights reserved. Convergence Theorems for Generalized Functional Sequences of Discrete-Time Normal Martingales Thu, 15 Oct 2015 12:13:34 +0000 The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale . A necessary and sufficient condition in terms of the Fock transform is obtained for such a sequence to be strongly convergent. A type of generalized martingales associated with is introduced and their convergence theorems are established. Some applications are also shown. Caishi Wang and Jinshu Chen Copyright © 2015 Caishi Wang and Jinshu Chen. All rights reserved. Recent Developments on Summability Theory and Its Applications Wed, 07 Oct 2015 07:27:59 +0000 Mikail Et, Mohammad Mursaleen, Syed Abdul Mohiuddine, Mahmut Işık, Jeff Connor, and Feyzi Başar Copyright © 2015 Mikail Et et al. All rights reserved. Unique Fixed Point Theorems for Generalized Contractive Mappings in Partial Metric Spaces Mon, 05 Oct 2015 08:59:38 +0000 We establish some unique fixed point theorems in complete partial metric spaces for generalized weakly -contractive mappings, containing two altering distance functions under certain assumptions. Also, we discuss some examples in support of our main results. Lakshmi Narayan Mishra, Shiv Kant Tiwari, Vishnu Narayan Mishra, and Idrees A. Khan Copyright © 2015 Lakshmi Narayan Mishra et al. All rights reserved. Performance on ICI Self-Cancellation in FFT-OFDM and DCT-OFDM System Mon, 05 Oct 2015 08:58:37 +0000 In orthogonal frequency division multiplexing (OFDM) system, the existence of frequency offset in AWGN channel affects the orthogonality among the subcarriers and consequently introduces the intercarrier interference (ICI). The paper investigates new ICI self-cancellation technique to mitigate the effect of ICI in FFT-OFDM and compares it to DCT based OFDM system in terms of bit error rate (BER) and carrier to interference ratio (CIR). The proposed method for group size three results in a significant 20 dB improved CIR in FFT-OFDM. In terms of BER, proposed ICI self-cancellation technique outperforms the other self-cancellation techniques in FFT-OFDM. Also, this paper investigates outperforming BER and CIR improvement by using DCT-OFDM without applying self-cancellation techniques, due to its energy compaction property. Shilpi Gupta, Upena Dalal, and Vishnu Narayan Mishra Copyright © 2015 Shilpi Gupta et al. All rights reserved. On Uniform Convergence of Sequences and Series of Fuzzy-Valued Functions Sun, 04 Oct 2015 11:50:45 +0000 The class of membership functions is restricted to trapezoidal one, as it is general enough and widely used. In the present paper since the utilization of Zadeh’s extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct for a fuzzy-valued function via related trapezoidal membership function. We derive uniform convergence of fuzzy-valued function sequences and series with some illustrated examples. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, we introduce the power series with fuzzy coefficients and define the radius of convergence of power series. Finally, by using the notions of H-differentiation and radius of convergence we examine the relationship between term by term H-differentiation and uniform convergence of fuzzy-valued function series. Uğur Kadak and Hakan Efe Copyright © 2015 Uğur Kadak and Hakan Efe. All rights reserved. Stability of Pexiderized Quadratic Functional Equation in Random 2-Normed Spaces Thu, 01 Oct 2015 13:19:50 +0000 The aim of this paper is to investigate the stability of Hyers-Ulam-Rassias type theorems by considering the pexiderized quadratic functional equation in the setting of random 2-normed spaces (RTNS), while the concept of random 2-normed space has been recently studied by Goleţ (2005). Mohammed A. Alghamdi Copyright © 2015 Mohammed A. Alghamdi. All rights reserved. Ulam-Hyers Stability of Trigonometric Functional Equation with Involution Thu, 01 Oct 2015 11:15:50 +0000 Let and be a commutative semigroup and a commutative group, respectively, and the sets of complex numbers and nonnegative real numbers, respectively, and or an involution. In this paper, we first investigate general solutions of the functional equation for all , where . We then prove the Hyers-Ulam stability of the functional equation; that is, we study the functional inequality for all , where and . Jaeyoung Chung, Chang-Kwon Choi, and Jongjin Kim Copyright © 2015 Jaeyoung Chung et al. All rights reserved. Fourier Expansions with Polynomial Terms for Random Processes Thu, 01 Oct 2015 08:40:49 +0000 Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also new for deterministic functions. Zhihua Zhang Copyright © 2015 Zhihua Zhang. All rights reserved. On the Classical Paranormed Sequence Spaces and Related Duals over the Non-Newtonian Complex Field Thu, 01 Oct 2015 08:29:31 +0000 The studies on sequence spaces were extended by using the notion of associated multiplier sequences. A multiplier sequence can be used to accelerate the convergence of the sequences in some spaces. In some sense, it can be viewed as a catalyst, which is used to accelerate the process of chemical reaction. Sometimes the associated multiplier sequence delays the rate of convergence of a sequence. In the present paper, the classical paranormed sequence spaces have been introduced and proved that the spaces are -complete. By using the notion of multiplier sequence, the α-, β-, and γ-duals of certain paranormed spaces have been computed and their basis has been constructed. Uğur Kadak, Murat Kirişci, and Ahmet Faruk Çakmak Copyright © 2015 Uğur Kadak et al. All rights reserved. Almost -Statistical and Strongly Almost -Convergence of Order of Sequences of Fuzzy Numbers Thu, 01 Oct 2015 08:27:37 +0000 The main purpose of this article is to introduce the concepts of almost -statistical convergence and strongly almost -convergence of order of sequences of fuzzy numbers with respect to an Orlicz function. We give some relations between strongly almost -convergence and almost -statistical convergence of order of sequences of fuzzy numbers. Mahmut Işık and Mikail Et Copyright © 2015 Mahmut Işık and Mikail Et. All rights reserved. The Characterization and Stability of g-Riesz Frames for Super Hilbert Space Wed, 30 Sep 2015 09:19:09 +0000 G-frames and g-Riesz frames as generalized frames in Hilbert spaces have been studied by many authors in recent years. The super Hilbert space has a certain advantage compared with the Hilbert space in the field of studying quantum mechanics. In this paper, for super Hilbert space , the definitions of a g-Riesz frame and minimal g-complete are put forward; also a characterization of g-Riesz frames is obtained. In particular, we generalize them to general super Hilbert space . Finally, a conclusion of the stability of a g-Riesz frame for the super Hilbert space is given. Dingli Hua and Yongdong Huang Copyright © 2015 Dingli Hua and Yongdong Huang. All rights reserved. Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means Mon, 28 Sep 2015 13:36:56 +0000 We present the best possible parameters and such that double inequalities , hold for all with , where , and are the arithmetic, second contraharmonic, and Toader means of and , respectively. Wei-Mao Qian, Ying-Qing Song, Xiao-Hui Zhang, and Yu-Ming Chu Copyright © 2015 Wei-Mao Qian et al. All rights reserved. Topological and Functional Properties of Some -Algebras of Holomorphic Functions Thu, 17 Sep 2015 13:35:41 +0000 Let    be the Privalov class of holomorphic functions on the open unit disk in the complex plane. The space equipped with the topology given by the metric defined by , , becomes an -algebra. For each , we also consider the countably normed Fréchet algebra of holomorphic functions on which is the Fréchet envelope of the space . Notice that the spaces and have the same topological duals. In this paper, we give a characterization of bounded subsets of the spaces and weakly bounded subsets of the spaces with . If denotes the strong dual space of and denotes the space of complex sequences satisfying the condition , equipped with the topology of uniform convergence on weakly bounded subsets of , then we prove that both set theoretically and topologically. We prove that for each    is a Montel space and that both spaces and are reflexive. Romeo Meštrović Copyright © 2015 Romeo Meštrović. All rights reserved. Multiple Solutions for Kirchhoff Equations under the Partially Sublinear Case Tue, 15 Sep 2015 09:53:33 +0000 We prove the infinitely many solutions to a class of sublinear Kirchhoff type equations by using an extension of Clark’s theorem established by Zhaoli Liu and Zhi-Qiang Wang. Wenjun Feng and Xiaojing Feng Copyright © 2015 Wenjun Feng and Xiaojing Feng. All rights reserved. Some Compactness and Interpolation Results for Linear Boltzmann Equation Mon, 07 Sep 2015 14:20:43 +0000 We discuss some compactness results in spaces related to the spectral theory of neutron transport equations for general classes of collision operators and Radon measures having velocity spaces as supports covering most physical models. We show in particular that the asymptotic spectrum of the transport operator is independent of . Nadjeh Redjel and Abdelkader Dehici Copyright © 2015 Nadjeh Redjel and Abdelkader Dehici. All rights reserved. Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces Wed, 02 Sep 2015 12:54:07 +0000 We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, if is in the Wiener amalgam space and is almost everywhere locally bounded, or , then strong -summability holds at each Lebesgue point of . The analogous results are given for Fourier series, too. Ferenc Weisz Copyright © 2015 Ferenc Weisz. All rights reserved. Shifting and Variational Properties for Fourier-Feynman Transform and Convolution Tue, 01 Sep 2015 11:32:03 +0000 Shifting, scaling, modulation, and variational properties for Fourier-Feynman transform of functionals in a Banach algebra are given. Cameron and Storvick's translation theorem can be obtained as a corollary of our result. We also study shifting, scaling, and modulation properties for the convolution product of functionals in . Byoung Soo Kim Copyright © 2015 Byoung Soo Kim. All rights reserved. Weighted Weak Local Hardy Spaces Associated with Schrödinger Operators Tue, 01 Sep 2015 06:28:38 +0000 We characterize the weighted weak local Hardy spaces related to the critical radius function and weights which locally behave as Muckenhoupt’s weights and actually include them, by the atomic decomposition. As an application, we show that localized Riesz transforms are bounded on the weighted weak local Hardy spaces. Hua Zhu Copyright © 2015 Hua Zhu. All rights reserved. Choi-Davis-Jensen Inequalities in Semifinite von Neumann Algebras Mon, 31 Aug 2015 11:41:25 +0000 We prove the Choi-Davis-Jensen type submajorization inequalities on semifinite von Neumann algebras for concave functions and convex functions. Turdebek N. Bekjan, Kordan N. Ospanov, and Asilbek Zulkhazhav Copyright © 2015 Turdebek N. Bekjan et al. All rights reserved. On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects Sun, 30 Aug 2015 08:23:40 +0000 We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result. Zuomao Yan Copyright © 2015 Zuomao Yan. All rights reserved. Functions of Bounded th -Variation and Continuity Modulus Sun, 23 Aug 2015 09:32:14 +0000 A scale of spaces exists connecting the class of functions of bounded th -variation in the sense of Riesz-Merentes with the Sobolev space of functions with -integrable th derivative. This scale is generated by the generalized functionals of Merentes type. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of smoothness of order . Odalis Mejía and Pilar Silvestre Copyright © 2015 Odalis Mejía and Pilar Silvestre. All rights reserved. Positive Solutions of Two-Point Boundary Value Problems for Monge-Ampère Equations Thu, 20 Aug 2015 08:52:48 +0000 This paper considers the following boundary value problem: , where is odd. We establish the method of lower and upper solutions for some boundary value problems which generalizes the above equations and using this method we present a necessary and sufficient condition for the existence of positive solutions to the above boundary value problem and some sufficient conditions for the existence of positive solutions. Baoqiang Yan and Meng Zhang Copyright © 2015 Baoqiang Yan and Meng Zhang. All rights reserved.